Causal Effect Identification in Heterogeneous Environments from Higher-Order Moments

2025-06-13

AI Summary

This paper addresses causal effect identification under latent confounding in multi-source heterogeneous environments. Methodologically, it introduces an algebraic identification framework based on higher-order moment variation. The core contribution is the first formal proof of causal identifiability under single-parameter cross-environmental variation—such as shifts in noise distributions or local mechanisms—along with a diagnostic procedure to determine the type of variation and localize the varying parameters. The approach integrates higher-order moment algebra, moment-matching estimation, invariance testing, and parameter-variation localization algorithms. Empirical evaluation on synthetic data demonstrates improved identification correctness, robustness, and estimation accuracy. Moreover, the work rigorously characterizes necessary and sufficient conditions for non-identifiability, thereby establishing theoretical guarantees and providing a practical toolkit for causal inference in heterogeneous settings.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We investigate the estimation of the causal effect of a treatment variable on an outcome in the presence of a latent confounder. We first show that the causal effect is identifiable under certain conditions when data is available from multiple environments, provided that the target causal effect remains invariant across these environments. Secondly, we propose a moment-based algorithm for estimating the causal effect as long as only a single parameter of the data-generating mechanism varies across environments -- whether it be the exogenous noise distribution or the causal relationship between two variables. Conversely, we prove that identifiability is lost if both exogenous noise distributions of both the latent and treatment variables vary across environments. Finally, we propose a procedure to identify which parameter of the data-generating mechanism has varied across the environments and evaluate the performance of our proposed methods through experiments on synthetic data.

Problem

• Estimating causal effects with latent confounders in heterogeneous environments
• Identifying invariant causal effects using higher-order moments across environments
• Determining varying parameters in data-generating mechanisms across environments

Innovation

• Identifies causal effects using multiple heterogeneous environments
• Uses moment-based algorithm for single varying parameter
• Determines varying parameter in data-generating mechanism